Experimental resolution of cooperative free energies for the ten ligation species of cobalt(II)/iron(II)-CO hemoglobin.

Cooperative free energies have been determined for the 10 ligation species of human hemoglobin in the Co(II)/Fe(II)-CO system. In this system, subunits containing unligated cobaltous hemes coexist in the same tetramer with naturally occurring ferrous hemes that are ligated with carbon monoxide. Tetramers comprising the 10 structurally unique combinations of ligated and unligated subunits were characterized in terms of their dimer-tetramer assembly free energies. By use of the thermodynamic linkage between assembly and ligation, the experimentally resolved values were used to obtain the corresponding cooperative free energies (i.e., the differences between actual free energies of ligation and the summed contributions of intrinsic values). The results obtained are in general accord with previous findings on this same system (Imai et al., 1980). The present study extends this earlier work by resolving the cooperative properties of each configurational isomer of the doubly ligated tetramers. The 10 ligation species were found to distribute into 5 discrete cooperative free energy levels according to a combinatorial code which includes, as a special case, the code found previously with cyanomethemoglobin and manganese-substituted hemoglobin (Smith et al., 1987; Daugherty et al., 1991). This distribution exhibits additional characteristics found in the oxygenation of normal ferrous hemoglobin including the quaternary enhancement effect (Mills & Ackers, 1979a,b). These results, and those of the following paper (Doyle et al., 1991), strongly support the premise that a common set of qualitative rules governs the cooperative interactions in hemoglobin irrespective of     

The energetics of ligand-linked subunit assembly in hemoglobin require a third allosteric structure

For partially ligated cyanomet hemoglobins, Smith and Ackers (Proc. Natl. Acad. Sci. U.S.A. 71 (1985) 4312) determined the free energies of dimer-tetramer assembly for all of the partially ligated species using a combination of kinetic and equilibrium methods. They found a third apparent cooperative free energy level in addition to those of deoxy- and cyanomethemoglobin. Using cryogenic methods, Perrella et al. (Biophys. Chem. 35 (1990) 97) confirmed the existence of the third cooperative free energy level, but found a different energy level assignment for one of the species. These combined studies have yielded a solid data base for considering mechanistic issues. The number of cooperative free energies delta Gc can, in principle, be different from the number of molecular forms which have unique free energies of heme-heme interaction, since delta Gc can be an average over conformational subspecies. Furthermore, since the delta Gc values are determined from free energies of dimer-tetramer assembly, it is necessary to evaluate possible contributions from dimeric properties, and from quaternary constraint (or enhancement) effects associated with subunit assembly. In this paper we analyze the observed distributions of apparent delta Gc values among the various ligation states in terms of mechanisms based on two interconvertible molecular forms (R and T) under the most general conditions in which (i) dimers may be cooperative, (ii) ligand affinities of alpha-subunits may be different within tetramers and dimers, and the same for beta-subunit affinities, and (iii) dimers need not be halves of R-state tetramers. It is found that the experimental distributions are inconsistent with even the most general model of the two-state class; thus, at least three molecular forms of tetramer are required, each with an individually different value of cooperative free energy (heme-heme interaction). This result implies the existence of at least three corresponding molecular structures; while a degeneracy of multiple structures into only a few dominant free energy levels is frequently to be expected, the reverse situation is extremely unlikely.     

Subunit hybridization studies of partially ligated cyanomethemoglobins using a cryogenic method. Evidence for three allosteric states

Reaction of tetrameric hemoglobin with ligands at the four heme sites yields nine species that have structurally unique combinations of ligated and unligated subunits. Using hemoglobins where the ligated subunits contain cyanomethemoglobin, Smith and Ackers studied the dimer-tetramer assembly reactions in all nine of the partially ligated species (F. R. Smith and G. K. Ackers, Proc. Natl. Acad. Sci. U.S.A. 82 (1985) 5347). They found a third assembly free energy in addition to those of unligated hemoglobin and fully ligated cyanomethemoglobin. The observed distribution of the three assembly free energies among the ten species was found to be incompatible with the two-state mechanism of allosteric control (J. Monod, J. Wyman and J. P. Changeaux, J. Mol. Biol. 12 (1965) 81). The results indicated a mechanism of 'combinatorial switching' in which the binding free energies per site change with configuration of occupied sites and not just their number. In this study, we have confirmed the existence of three assembly free energies among the ten ligation species using a cryogenic method (M. Perrella and L. Rossi-Bernardi, Methods Enzymol. 76 (1981) 133). For one of the species we find a different free energy assignment from that reported by Smith and Ackers; for all other species we observe the same assignments as in earlier work. The revised distribution also requires a 'combinatorial' mechanism of allosteric switching among the three states.     

What the intermediate compounds in ligand binding to hemoglobin tell about the mechanism of cooperativity

The populations of the intermediates in concentrated solutions of hemoglobin A0 equilibrated at various PCO values, pH 7.0, 0.1 M KCl, and 20 degrees C, have been determined using cryogenic methods. Data on CO saturations and distributions of intermediates were analysed in terms of the free energies of dimer-tetramer assembly of the intermediates (G.K. Ackers and F.R. Smith, Annu. Rev. Biophys. Chem. 16 (1987) 583). The cooperative free energy value of the singly ligated species was approximately one-half the total cooperative energy. The cooperative free energy value of the doubly ligated species was not significantly different from that of carboxyhemoglobin. Because of experimental error, the observed difference in concentrations among the populations of the doubly ligated species cannot be taken as indicative of their functional heterogeneity. Additional studies on some NO intermediates have emphasized that (alpha 1 beta 1)(alpha 2 beta 2)X, a key intermediate in the formulation of the 'third-state' hypothesis in the deoxy/cyanomethemoglobin system, has a free energy value for dimer-tetramer assembly which is critically dependent on the nature of the ligand X as suggested by Ackers and Smith (reference as cited above).     

Cooperative free energies for nested allosteric models as applied to human hemoglobin.

A model is developed for ligand binding to human hemoglobin that describes the detailed cooperative free-energies for each of the ten different ligated (cyanomet) species as observed by Smith and Ackers (Smith, F.R., and G.K. Ackers. 1985. Proc. Natl. Acad. Sci. USA.82:5347-5351). The approach taken here is an application of the general principle of hierarchical levels of allosteric control, or nesting, as suggested by Wyman (Wyman, J. 1972. Curr. Top. Cell. Reg. 6:207-223). The model is an extension of the simple two-state MWC model (Monod, J., J. Wyman, and J.P. Changeux. 1965. J. Mol. Biol. 12:88-118) using the idea of cooperative binding within the T (deoxy) form of the macromolecule, and has recently been described as a "cooperon" model (Di Cera, E. 1985. Ph.D. thesis). The T-state cooperative binding is described using simple interaction rules first devised by Pauling (Pauling, L. 1935. Proc. Natl. Acad. Sci. USA. 21:186-191). In this application three parameters suffice to describe the cooperative free-energies of the 10 ligated species of cyanomet hemoglobin. The redox process in the presence of cyanide, represented as a Hill plot, is simulated from Smith and Ackers' cooperative free-energies and is compared with available electrochemical binding measurements.     

Hemoglobin/O2 systems: mechanistic discrimination based on Ackers' model

The kinetics of the reaction of hemoglobin with molecular oxygen, in which rapid mixing is followed by a fast temperature jump, is numerically simulated. We use the system of Ackers (1998) which distinguishes four forms of bi-ligated hemoglobin. The data suggest the involvement of isomerization steps for bi- and triliganded hemoglobin. Our first model assumes a linear addition of oxygen with one path to and from each bi-ligated species. Our second model allows cross-overs between paths, as described by Ackers (1998). Our third model exploits the observation (Perrella et al., 1990) that two of the four bi-ligated forms are at low concentration. We explore whether these models can be distinguished experimentally. We find a narrow oxygen concentration range where Models 1 and 2 can be distinguished by rapid flow experiments. The distinction between Models 2 and 3 is larger in stopped flow experiments within a limited oxygen concentration range but not easily detectable in chemical relaxation following rapid flow. The detection of two special states of free hemoglobin may be possible at low oxygen concentration. However, the step reaction free enthalpy (or Gibbs free energy) values make it more likely that two special states are present in fully ligated hemoglobin.     

Tetramer-dimer dissociation in homoglobin and the Bohr effect.

The pH dependence of the apparent tetramer to dimer dissociation constant has been determined at 20 degrees for both oxy- and deoxyhemoglobins A and Kansas. These measurements were made by three different procedures: gel chromatography, sedimentation velocity, and kinetic methods in either of three buffer systems: 0.05 M cacodylate, Tris, or glycine with 1 mM EDTA and 0.1 M NaCl between pH 6.5 and 11. The tetramer-dimer dissociation constant of human oxyhemoglobin A decreases from about 3.2 X 10(-6) M at pH 6.0 to about 3.2 X 10(-8) M at pH 8.5. The slope of this line indicates that the dissociation of tetramer to dimer is accompanied by the uptake of about 0.6 protons per mol of tetramer in this region. The corresponding dissociation constant for deoxyhemoglobin in the same pH region increases apparently almost linearly from 1.0 x 10(-12) M at pH 6.5 to about 1.0 x 10(-5) M at pH 11. To dimer is associated with the release of about 1.6 protons per mol of tetramer. Comparison of these data with the known proton release accompanying the oxygenation of tetramers confirms that the pH dependence of oxygen binding by dimers must be very small. The present data predict that the overall proton release or uptake per oxygen bound by dimer should be less than 0.1. The tetramer-dimer dissociation equilibria of oxy- and deoxyhemoglobins above pH 8.5 have identical pH dependences. In this range the dissociation constant of deoxy-Hb is about one-tenth that of oxyhemoglobin. Human oxyhemoglobin Kansas is known to have an enhanced tetramer-dimer dissociation compared with that of hemoglobin A. Below pH 8.5 the tetramer-dimer dissociation constant of Hb Kansas is about 400 times greater than that of HbA in the absence of phosphate buffers. In contrast, the tetramer-dimer dissociation constants of deoxyhemoglobins A and Kansas appear to be identical. These findings are consistent with previous structural observations on these hemoglobins. The data on the tetramer-dimer dissociation of human hemoglobin were used to calculate the total free energy of binding of oxygen to the tetramer and the median oxygen pressure on the basis of fundamental linkage relations and a pH-independent estimate of the total free energy of binding oxygen to dimer. Simulated oxygen binding curves were generated with the equations of Ackers and Halvorson (Ackers, G. K., and Halvorson, H. (1974) Proc. Natl. Acad. Sci. U.S.A. 71, 4312-4316) by making two assumptions: (a) that the dimers are noncooperative and pH-independent in O2 binding and (b) that the distribution of cooperative energy in the oxygenation of tetramers is independent of pH. We have compared these simulations with experimental data obtained at low protein concentrations (30 to 124 muM heme) to show that the variation in oxygen affinity with pH can be described in terms of the subunit equilibria. We conclude that an accurate analysis of the contributions of individual oxygen binding steps to the Bohr effect cannot be made without considering the contributions of the dimers to oxygen binding...     

The molecular code for hemoglobin allostery revealed by linking the thermodynamics and kinetics of quaternary structural change. 1. Microstate linear free energy relations

A novel model linking the thermodynamics and kinetics of hemoglobin's allosteric (R --> T) and ligand binding reactions is applied to photolysis data for human HbCO. To describe hemoglobin's kinetics at the microscopic level of structural transitions and ligand-binding events for individual [ij]-ligation microstates ((ij)R --> (ij)T, (ij)R + CO --> ((i)(+1))(k)R, and (ij)T + CO --> ((i)(+1))(k)T), the model calculates activation energies, (ij)DeltaG(++), from previously measured cooperative free energies of the equilibrium microstates (Huang, Y., and Ackers, G. K. (1996) Biochemistry 35, 704-718) by using linear free energy relations ((ij)DeltaG(++) - (01)DeltaG(++) = alpha[(ij)DeltaG - (01)DeltaG], where the parameter alpha, describing the variation of activation energy with reaction energy perturbation, can depend on the natures of both the reaction and the perturbation). The alpha value measured here for the allosteric dynamics, 0.21 +/- 0.03, corresponds closely to values observed previously, strongly suggesting that the thermodynamic microstate energies directly underlie the allosteric kinetics (as opposed to the alpha((ij)DeltaG(RT)) serving merely as arbitrary fitting parameters). Besides systematizing the study of hemoglobin kinetics, the utility of the microstate linear free energy model lies in the ability to test microscopic aspects of allosteric dynamics such as the "symmetry rule" for quaternary change deduced previously from thermodynamic evidence (Ackers, G. K., et al. (1992) Science 255, 54-63). Reflecting a remarkably detailed correspondence between thermodynamics and kinetics, we find that a kinetic model that includes the large free energy splitting between doubly ligated T microstates implied by the symmetry rule fits the data significantly better than one that does not.     

Energetics of subunit assembly and ligand binding in human hemoglobin.

An extensive and self-consistent set of thermodynamic properties has recently been established for the coupled processes of subunit assembly and ligand binding (oxygen and protons) in human hemoglobin. The resulting thermodynamic values permit a consideration of the possible sources of energetic terms accounting for stability of the tetrameric quaternary structures at different stages of ligation, and of the possible sources of cooperative energy. The analysis indicates that: (a) The change in buried surface ara upon oxygenation (i.e., hydrophobic stabilization) does not play a dominant role in stabilizing the unliganded tetramer relative to the liganded tetramer. (b) The pattern of enthalpic and entropic contributions to the free energies of dimer-tetramer. (c) The thermodynamic results are consistent with a dominant role of increased hydrogen bond formation in the deoxy quaternary structure. (d) Within tetramers the variation in free energy for successive oxygenation steps arises from both enthalpic and entropic contributions and the enthalpic contributions are almost entirely attributable to the heats of Bohr proton release. At pH 7.4 the pattern of thermodynamic values suggests that a large contribution to the free energy of cooperativity may arise from the energetics of Bohr proton release. It is suggested that a combination of proton ionization and hydrogen bonding may account for the main energetic features of cooperativity. Possible contributions from fluctuation behavior cannot presently be evaluated.     

Linked functions in allosteric proteins: Extension of the concerted (MWC) model for ligand-linked subunit assembly and its application to human hemoglobins

The allosteric model of Monod et al. (1965) (MWC) has been extended to take into account the effects of subunit dissociation. The problem is formulated theoretically in terms of a general model for two allosteric species (dimers and tetramers) linked by a polymerization reaction. Relationships are presented for interpreting the dimer-tetramer association constants in terms of allosteric model parameters.Sub-cases of the general model were tested against recent experimental data on the oxygenation-linked dimer-tetramer equilibria in normal human hemoglobin and in the variant hemoglobin Kansas (β₁₀₂, Asp → Thr). The objectives of these analyses were: (1) to find the simplest models capable of describing the linked dimer-tetramer equilibria in the two hemoglobin systems, and (2) to evaluate the corresponding model parameters so that allosteric properties of the two hemoglobins may be compared.In the simplest version of the model, the dimer is half of an R-state tetramer. This model was found to be excluded unequivocally by the data for both normal hemoglobin and hemoglobin Kansas when the α and β chains have equal binding affinities. When this two-state model was modified to permit non-equivalent affinities for the chains, the model could be fitted to hemoglobin Kansas, but not to hemoglobin A. A model, in which the dimers are allowed to exist in a state different from the tetramer R state, was found to be consistent with the data for hemoglobin A, with equivalent binding by the α and β chains. For hemoglobin A, the unliganded R-state tetramers have a different subunit dissociation energy from that of fully liganded R-state tetramers. The simplest model capable of describing both hemoglobin A and hemoglobin Kansas was obtained by extending this three-state model to permit (but not require) functional non-equivalence of the α and β chains. For these MWC models, unique estimates were obtained for the model parameters.The allosteric constants for tetrameric hemoglobins A and Kansas are approximately equal. The value obtained from hemoglobin A is similar to previous estimates, whereas the value for hemoglobin Kansas is lower than previously estimated (Edelstein, 1971) by approximately two orders of magnitude. The low affinity of hemoglobin Kansas tetramer does not arise from an unusually high allosteric constant favoring the T-state species. It is largely the consequence of a greatly reduced oxygen affinity of β chains in the T state, and reduced values for the ratio between affinities in the R and T states.     

Functional properties of human hemoglobins synthesized from recombinant mutant beta-globins.

The previous and following articles in this issue describe the recombinant synthesis of three mutant beta-globins (beta 1 Val----Ala, beta 1 Val----Met, and the addition mutation beta 1 + Met), their assembly with heme and natural alpha chains into alpha 2 beta 2 tetramers, and their X-ray crystallographic structures. Here we have measured the equilibrium and kinetic allosteric properties of these hemoglobins. Our objective has been to evaluate their utility as surrogates of normal hemoglobin from which further mutants can be made for structure-function studies. The thermodynamic linkages between cooperative oxygenation and dimer-tetramer assembly were determined from global regression analysis of multiple oxygenation isotherms measured over a range of hemoglobin concentration. Oxygen binding to the tetramers was found to be highly cooperative (maximum Hill slopes from 3.1 to 3.2), and similar patterns of O2-linked subunit assembly free energies indicated a common mode of cooperative switching at the alpha 1 beta 2 interface. The dimers were found to exhibit the same noncooperative O2 equilibrium binding properties as normal hemoglobin. The most obvious difference in oxygen equilibria between the mutant recombinant and normal hemoglobins was a slightly lowered O2 affinity. The kinetics of CO binding and O2 dissociation were measured by stopped-flow and flash photolysis techniques. Parallel studies were carried out with the mutant and normal hemoglobins in the presence and absence of organic phosphates to assess their allosteric response to phosphates. In the absence of organic phosphates, the CO-binding and O2 dissociation kinetic properties of the mutant dimers and tetramers were found to be nearly identical to those of normal hemoglobin. However, the effects of organic phosphates on CO-binding kinetic properties of the mutants were not uniform: the beta 1 + Met mutant was found to deviate somewhat from normalcy, while the beta 1 Val----Met mutant reproduced the native allosteric response. Further characterization of the allosteric properties of the beta 1 Val----Met mutant was made by measuring the pH dependence of its overall oxygen affinity by tonometry. Regulation of oxygen affinity by protons was found to be nearly identical to normal hemoglobin from pH 5.8 to 9.3 (0.52 +/- 0.07 protons released per oxygen bound at pH 7.4). The present study demonstrates that the equilibrium and kinetic functional properties of the recombinant beta 1 Val----Met mutant mimic reasonably well those of normal hemoglobin. We conclude that this mutant is well-suited to serve as a surrogate system of normal hemoglobin in the production of mutants for structure-function studies.     

Allosteric interpretation of the oxygen-binding reaction of human hemoglobin tetramers

An allosteric model is presented that provides a simple explanation for the low population of triply ligated species, relative to the other species, in the oxygenation of human hemoglobin tetramers as found in high-concentration studies [Gill, S. J., Di Cera, E., Doyle, M. L., Bishop, G. A., & Robert, C. H. (1987) Biochemistry (preceding paper in this issue)]. The model is a quantitative interpretation of the Perutz mechanism [Perutz, M. F. (1970) Nature (London) 228, 726-739] and is based on a number of structural and thermodynamic findings so far reported in the analysis of hemoglobin properties. Human hemoglobin is assumed to exist in two quaternary states: the T or low-affinity state and the R or high-affinity state. An extreme chain heterogeneity in the T state is postulated so that oxygen binds only to the alpha chains. Nearest-neighbor interactions between the alpha chains may lead to cooperativity within the T state. The R state is noncooperative, and both the alpha and beta chains have equal oxygen affinity.     

Mutagenic dissection of hemoglobin cooperativity: effects of amino acid alteration on subunit assembly of oxy and deoxy tetramers.

Free energies of oxygen-linked subunit assembly and cooperative interaction have been determined for 34 molecular species of human hemoglobin, which differ by amino acid alterations as a result of mutation or chemical modification at specific sites. These studies required the development of extensions to our earlier methodology. In combination with previous results they comprise a data base of 60 hemoglobin species, characterized under the same conditions. The data base was analyzed in terms of the five following issues. (1) Range and sensitivity to site modifications. Deoxy tetramers showed greater average energetic response to structural modifications than the oxy species, but the ranges are similar for the two ligation forms. (2) Structural localization of cooperative free energy. Difference free energies of dimer-tetramer assembly (oxy minus deoxy) yielded delta Gc for each hemoglobin, i.e., the free energy used for modulation of oxygen affinity over all four binding steps. A structure-energy map constructed from these results shows that the alpha 1 beta 2 interface is a unique structural location of the noncovalent bonding interactions that are energetically coupled to cooperativity. (3) Relationship of cooperativity to intrinsic binding. Oxygen binding energetics for dissociated dimers of mutants strongly indicates that cooperativity and intrinsic binding are completely decoupled by tetramer to dimer dissociation. (4) Additivity, site-site coupling and adventitious perturbations. All these are exhibited by individual-site modifications of this study. Large nonadditivity may be correlated with global (quaternary) structure change. (5) Residue position vs. chemical nature. Functional response is solely dictated by structural location for a subset of the sites, but varies with side-chain type at other sites. The current data base provides a unique framework for further analyses and modeling of fundamental issues in the structural chemistry of proteins and allosteric mechanisms.     

Description of the molecular mechanism of cooperativity in human hemoglobin cannot be limited to a first-order free energy coupling concept

Studies of the linkage between ligand binding and subunit assembly of oligomeric proteins have extensively used the concept of free energy coupling. The "order" of these free energy couplings was introduced [Weber, G. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 7098-7102] as the number of subunits that must be liganded to alter specific intersubunit interactions. This concept dictates that the ligation of fewer subunits has no effect, but once the order number of subunits becomes ligated, the specific intersubunit interaction energy between those particular subunits is completely eliminated. Weber's report claims that the free energy coupling between oxygen binding and the dimer-tetramer subunit assembly in stripped human hemoglobin A is "first order". This conclusion is based on the analysis of a set of previously published equilibrium constants [Mills, F. C., Johnson, M. L., & Ackers, G. K. (1976) Biochemistry 15, 5350-5362]. I subsequently reported that the original experimental data, from which the equilibrium constants were derived, are consistent with both the first-order and "second-order" free energy coupling concepts [Johnson, M. L. (1986) Biochemistry 25, 791-797]. I also demonstrated that more precise recent experimental data [Chu, A. H., Turner, B. W., & Ackers, G. K. (1984) Biochemistry, 23, 604-617] are consistent with both the first-order and second-order free energy coupling concepts. A recent article [Weber, G. (1987) Biochemistry 26, 331-332] disagrees that the oxygen-binding data for human hemoglobin A are consistent with a second-order model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Direct and indirect pathways of functional coupling in human hemoglobin are revealed by quantitative low-temperature isoelectric focusing of mutant hybrids

Functional energetic coupling within human hemoglobin has been explored by using quantitative analysis of asymmetric mutant hybrid equilibria. Previous work showed that the free energy of cooperativity is largely attributable to alterations in free energy that accompany changing interactions at the interface between alpha 1 beta 1 and alpha 2 beta 2 dimers [Pettigrew et al. (1982) Proc. Natl. Acad. Sci. U.S.A. 79, 1849]. However, the issue of how cooperativity-linked sites in the molecule are energetically coupled in manifesting cooperative ligation is still not well delineated. In this paper we address the questions of what types of functional coupling pathways are operational in hemoglobin, what some of their characteristics are, and how they are related to one another. By constructing asymmetric mutant hybrid hemoglobins, we can assay how two structurally identical, symmetrically equivalent sites are energetically coupled in manifesting subunit assembly and/or cooperative ligation. Asymmetric hybrid hemoglobins, i.e., those containing a single modified site, cannot be isolated and must be studied in equilibrium with their symmetric parent molecules. In order to study these asymmetric hybrid equilibria, we have developed new theory and quantitation techniques to augment the low-temperature quenching and isoelectric focusing procedures of Perrella et al. [(1978) Anal. Biochem. 88, 212]. Studies of these mutant hybrid hemoglobins have provided evidence for three distinct types of energetic coupling within the hemoglobin tetramer. All alpha 1 beta 2 interface sites examined are involved in cooperativity-linked indirect coupling. Within the context of this indirect "pathway" there exist two different types of direct long-range coupling. One of these classes of direct long-range pathways is linked to cooperative ligand binding while the other class is not.     

Single-site modifications of half-ligated hemoglobin reveal autonomous dimer cooperativity within a quaternary T tetramer

The patterns of energetic response elicited by single-site hemoglobin mutations and chemical mocdifications have been determined in order to probe the dimer–dimer interface of the half-ligated tetramer (species[21]) that was previously shown to behave as allosterically distinct from both the unligated and fully ligated molecules¹. In this study the free energies of quaternary assembly(dimers to tetramers) were determined for aseries of 24 tetrameric species in which one dimeric half-molecule is ligated while the adjacent αβ dimer is unligated and contains a single amino acid modification. Assembly energies have also been determined for tetramers bearing the same amino acid modifications but where the hemesites were completely vacant and additionally where they were fully occupied. A total of 72 molecular species were thus characterized. It was found that mutationally induced perturbations to the free energy of quaternary assembly were identical for the half-ligated tetramers and the unligated tetramers over the entire spatial distrubution of altered sites, but exhibited a radically different pattern from that of the fully ligated molecules. These results indicate that the dimer–dimer interface of the half-ligated tetramer(species[21]) has the same quaternary sturcture as that of the unligated molecule, i.e, “quaternary T.” This quaternary structure assignment of species [21] strongly supports the operation of a Symmetry Rule which translates changes in hemesite ligation into six T → R quaternary switchpoints². Analysis of the observed Symmetry Rule behaviour in relation to the measured distribution of cooperative free energies for the partially ligated species reveals significant cooperativity between α and β subunits of the dimeric half-tetramer within quaternary T. The mutational results indicate that these interactions are not “paid for” by breaking or making noncovalent bonds at the dimer–dimer interface (α¹β²). They arise from structural and energetic changes that are “internal” to the ligated dimer even though its association with the unligated dimer is required for the cooperativity to occur. Free energy of “tertiary constraint” is thus generated by the first binding step and is propagated to the second hemesite while the dimer–dimer interface α¹β²serves as a constraint. The “sequential” cooperativity that occurs within the half-molecule is thus preconditioned by the constraint of a quaternary T interface; release of this constraint by dissociation produces only noncooperative dimers. When the constraint is released functionally by T to R dimer rearrangement (at each switch-point specified by the a Symmetry Rule) the alterations of interfacial bonds then dominate the energetics of cooperativity. © 1993 Wiley-Liss, Inc.     

Cooperative oxygen binding, subunit assembly, and sulfhydryl reaction kinetics of the eight cyanomet intermediate ligation states of human hemoglobin.

Correlations between the energetics of cooperativity and quaternary structural probes have recently been made for the intermediate ligation states of Hb [Daugherty et al. (1991) Proc. Natl. Acad. Sci. US 88, 1110-1114]. This has led to a "molecular code" which translates configurations of the 10 ligation states into switch points of quaternary transition according to a "symmetry rule"; T-->R quaternary structure change is governed by the presence of at least one heme-site ligand on each of the alpha beta dimeric half-molecules within the tetramer [see Ackers et al. (1992) Science 255, 54-63, for summary]. In order to further explore this and other features of the cooperative mechanism, we have used oxygen binding to probe the energetics and cooperativities for the vacant sites of the cyanomet ligation species. We have also probed structural aspects of all eight cyanomet ligation intermediates by means of sulfhydryl reaction kinetics. Our oxygen binding results, obtained from a combination of direct and indirect methods, demonstrate the same combinatorial aspect to cooperativity that is predicted by the symmetry rule. Overall oxygen affinities of the two singly-ligated species (alpha +CN beta)(alpha beta) and (alpha beta +CN)(alpha beta) were found to be identical (pmedian = 2.4 Torr). In contrast, the doubly-ligated species exhibited two distinct patterns of oxygen equilibria: the asymmetric species (alpha +CN beta +CN)(alpha beta) showed very high cooperativity (nmax = 1.94) and low affinity (pmedian = 6.0 Torr), while the other three doubly-ligated species showed diminished cooperativity (nmax = 1.23) and considerably higher oxygen affinity (pmedian = 0.4 Torr). Extremely high oxygen affinities were found for the triply-ligated species (alpha +CN beta +CN)(alpha beta +CN) and (alpha +CN beta +CN)(alpha +CN beta) (pmedian = 0.2 Torr). Their oxygen binding free energies are considerably more favorable than those of the alpha and beta subunits within the dissociated alpha beta dimer, demonstrating directly the quaternary enhancement effect, i.e., enhanced oxygen affinity at the last binding step of tetramer relative to the dissociated protomers. Oxygen binding free energies measured for the alpha subunit within the isolated (alpha beta +CN) dimer and for the beta subunit within the isolated (alpha +CN beta) dimer sum to the free energy for binding two oxygens to normal hemoglobin dimers (-16.3 +/- 0.2 versus -16.7 +/- 0.2, respectively), arguing against cooperativity in the isolated dimer. Correlations were established between cooperative free energies of the 10 cyanomet ligation microstates and the kinetics for reacting their free sulfhydryl groups.(ABSTRACT TRUNCATED AT 400 WORDS)     

Oxygen binding and subunit interaction of hemoglobin in relation to the two-state model

Mills and Ackers (Mills, F.C., and Ackers, G.K. (1979) J. Biol. Chem. 254, 2881-2887) have reported the subunit interactions of hemoglobin to decrease on binding of the fourth molecule of oxygen to hemoglobin. This effect, which they called quaternary enhancement, is incompatible with the two-state Monod, Wyman, and Changeux allosteric model. Their free energy of binding of the fourth molecule (-9.3 kcal/mol) has been compared with independent kinetic estimates which give -8.6 kcal/mol. This smaller value is consistent with literature values and allows reasonable representation of the equilibrium curve using the two-state model without invoking quaternary enhancement.     

Computationally accessible method for estimating free energy changes resulting from site-specific mutations of biomolecules: systematic model building and structural/hydropathic analysis of deoxy and oxy hemoglobins

A practical computational method for the molecular modeling of free-energy changes associated with protein mutations is reported. The de novo generation, optimization, and thermodynamic analysis of a wide variety of deoxy and oxy hemoglobin mutants are described in detail. Hemoglobin is shown to be an ideal candidate protein for study because both the native deoxy and oxy states have been crystallographically determined, and a large and diverse population of its mutants has been thermodynamically characterized. Noncovalent interactions for all computationally generated hemoglobin mutants are quantitatively examined with the molecular modeling program HINT (Hydropathic INTeractions). HINT scores all biomolecular noncovalent interactions, including hydrogen bonding, acid-base, hydrophobic-hydrophobic, acid-acid, base-base, and hydrophobic-polar, to generate dimer-dimer interface "scores" that are translated into free-energy estimates. Analysis of 23 hemoglobin mutants, in both deoxy and oxy states, indicates that the effects of mutant residues on structurally bound waters (and visa versa) are important for generating accurate free-energy estimates. For several mutants, the addition/elimination of structural waters is key to understanding the thermodynamic consequences of residue mutation. Good agreement is found between calculated and experimental data for deoxy hemoglobin mutants (r = 0.79, slope = 0.78, standard error = 1.4 kcal mol(-1), n = 23). Less accurate estimates were initially obtained for oxy hemoglobin mutants (r = 0.48, slope = 0.47, standard error = 1.4 kcal mol(-1), n = 23). However, the elimination of three outliers from this data set results in a better correlation of r = 0.87 (slope = 0.72, standard error = 0.75, n = 20). These three mutations may significantly perturb the hemoglobin quaternary structure beyond the scope of our structural optimization procedure. The method described is also useful in the examination of residue ionization states in protein structures. Specifically, we find an acidic residue within the native deoxy hemoglobin dimer-dimer interface that may be protonated at physiological pH. The final analysis is a model design of novel hemoglobin mutants that modify cooperative free energy (deltaGc)--the energy barrier between the allosteric transition from deoxy to oxy hemoglobin.